What is the best way to know what amino-acid that is replicated by mRNA codon?
ex: what is the best way to know that AUG codon produces Metionin? (if I'm not mistaken). Does it means that I have to remember all the 64 triplets of synonymus codon in my biology dictionary?

As far as I know yes. Of course there is this 3 entry table that helps remembreing some synonymous codons, but there is no logical shorcut for it.
But what's the point? The only one you really need to know are start and stop codons. For the othr, well, you've got you book

As far as I've read my bio book...Actually you can determine what is the amino-acids from their characteristics...example like you can determine some amino-acids by seeing the last nitrogenic bases at the codon (pyrimidine or purine). From there you'll only know whether the amino-acids are hydrofobic or hydrofilic...no specific name in it...

All nice and dandy. Until you get the olympics and you get a question like "What protein sequence will you get from the following DNA generative cathene- ATGCCAGTCAGTAACGTAGCAGATACAGATACAGGGATGACCCAGTAGATGAGAGATGCACAGCATGACTGAC" And then you will wish you will have studied that table

"As a biologist, I firmly believe that when you're dead, you're dead. Except for what you live behind in history. That's the only afterlife" - J. Craig Venter

You are right Patrick. It is useless. But you have to realise one thing: practically my only chance of getting out of this damned country and to study in a prestiogious university in th US is having at least a bronze medal at IBO. But in order to qualify for Nationals i had to memorise the genetic code. If that is the stupid junk i need to do in order to acomplisg my dream, than so be it!

"As a biologist, I firmly believe that when you're dead, you're dead. Except for what you live behind in history. That's the only afterlife" - J. Craig Venter

I do not say that you are stupid to do it, I say that whoever came with this kind of question is stupid. Science has nothing to do with this kind of things. A good scientist is not someone who knows a lot (no human can know enough know) but someone who is able to use his knoledge to search for the relevant dat when they are needed. Internet and Library are here to contain the data, brains can be better used as cross referencing them and devising and analyzing results.

But good luck for the IBO, i wish you can get out of Romania, if it is what suits you. But Why prestigious university in the US? Europe also has some great university, which are also usually much cheaper.